A process capability index is a measure that evaluates the behavior of a product or process characteristics related to the engineering specification. In the literature, many articles can be found about capability indices for both symmetric and asymmetric tolerance. In this article, we introduce a new class of indices, C′′′p(u, v), for the processes with asymmetric tolerance. In addition, we study the relation between this index and the departure ratio of the process centering, as well as, the relation between this index and the upper bound of the percentage of non-conforming products. Based on these results we suggest a criteria for choosing an index from the under investigation class. To guide practitioners, numerical examples are provided.

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